gameanalysis.fixedpoint module¶
Module for finding fixed points of functions on a simplex
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gameanalysis.fixedpoint.
fixed_point
(func, init, **kwargs)[source]¶ Compute an approximate fixed point of a function
Parameters: - func (ndarray -> ndarray) – A continuous function mapping from the d-simplex to itself.
- init (ndarray) – An initial guess for the fixed point. Since many may exist, the choice of starting point will affect the solution.
- kwargs (options) – Additional options to pass on to labeled_subsimplex. See other options for details.
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gameanalysis.fixedpoint.
labeled_subsimplex
(label_func, init, disc)[source]¶ Find approximate center of a fully labeled subsimplex
This runs once at the discretization provided. It is recommended that this be run several times with successively finer discretization and warm started with the past result.
Parameters: - label_func (ndarray -> int) – A proper lableing function. A labeling function takes an element of the d-simplex and returns a label in [0, d). It is proper if the label always coresponds to a dimension in support.
- init (ndarray) – An initial guess for where the fully labeled element might be. This will be projected onto the simplex if it is not already.
- disc (int) – The discretization to use. Fixed points will be approximated by the reciprocal this much.
Returns: ret – A discretized simplex with 1 coarser resolution (i.e. ret.sum() + 1 == init.sum()) that is fully labeled.
Return type: ndarray
Notes
This is an implementation of the sandwhich method from [5] and [6]
[5] Kuhn and Mackinnon 1975. Sandwich Method for Finding Fixed Points. [6] Kuhn 1968. Simplicial Approximation Of Fixed Points.